A closed-form solution to the forward displacement analysis of a Schönflies parallel manipulator

The forward displacement analysis (FDA) in closed form of two classes of new parallel mechanisms derived from the Stewart Platform Mechanism (SPM) is presented in this paper. These mechanisms, when a set of actuator displacements is given, become multiloop structures of type PRR-3S and PPR-3S, with P, R and S for prismatic, revolute and spherical pairs, whereas the SPM has the structure RRR-3S. Solving the FDA in closed form means finding all the possible positions and orientations of the output controlled link when a set of actuator displacements is given, or equivalently, finding all possible closures of the corresponding structure. The closed form analysis of the PRR-3S and PPR-3S structures here presented results in algebraic equations in one unknown of degree 16 and 12, respectively. Hence 16 and 12 closures of the corresponding structures can be obtained. Numerical examples confirm these new theoretical results.

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Mobility and Position Analysis of a Novel 3-DOF Translational Parallel Mechanism

Volume 2: 30th Annual Mechanisms and Robotics Conference, Parts A and B ◽

10.1115/detc2006-99031 ◽

2006 ◽

Cited By ~ 1

Author(s):

Daxing Zeng ◽

Zhen Huang ◽

Linlin Zhang

Keyword(s):

Closed Form ◽

Parallel Mechanism ◽

Parallel Manipulator ◽

Continuation Method ◽

Mobility Analysis ◽

Forward Displacement ◽

Displacement Analysis ◽

Displacement Problem ◽

Numerical Example ◽

Forward Displacement Analysis

This paper presents the mobility analysis, the inverse and forward displacement analysis, and workspace of a novel 3-DOF 3-RPUR parallel manipulator. Closed-form inverse displacement solutions are obtained by the Denavit-Hartenberg method. The forward displacement problem is analyzed by using the continuation method and proved applying the result of the inverse displacement analysis. The workspace of the mechanism is also obtained. A numerical example is given in the paper.

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Jerk analysis of a module of an artificial spine by means of screw theory

Journal of Applied Research and Technology ◽

10.22201/icat.16656423.2009.7.03.484 ◽

2009 ◽

Vol 7 (03) ◽

Author(s):

J. Gallardo-Alvarado ◽

R. Lesso-Arroyo

Keyword(s):

Closed Form ◽

Parallel Manipulator ◽

Screw Theory ◽

Closed Form Solution ◽

Form Solution ◽

Displacement Analysis

In this work, a novel parallel manipulator is introduced with the purpose of simulating the jerk analysis of the end of the spine.The displacement analysis is presented in a semi-closed form solution whereas the velocity, acceleration and jerk analyses are carried out by means of the theory of screws.

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A novel three degrees of freedom partially decoupled robot with linear actuators

Robotica ◽

10.1017/s026357471100083x ◽

2011 ◽

Vol 30 (3) ◽

pp. 467-475 ◽

Cited By ~ 8

Author(s):

Jaime Gallardo-Alvarado ◽

Gürsel Alici ◽

Ramón Rodríguez-Castro

Keyword(s):

Degrees Of Freedom ◽

Control Point ◽

Closed Form Solution ◽

Parallel Manipulators ◽

Form Solution ◽

End Effector ◽

Forward Displacement ◽

Displacement Analysis ◽

Common Control ◽

Forward Displacement Analysis

SUMMARYIn this work, a new translational robot formed with two different parallel manipulators with a common control point is introduced. An asymmetric parallel manipulator provides three translational degrees of freedom to the proposed robot while the orientation of the end-effector platform is kept constant by means of a Delta-like manipulator. An exact solution is easily derived to solve the forward displacement analysis while a semi-closed form solution is available for solving the inverse displacement analysis. The infinitesimal kinematics of the robot is approached by applying the theory of screws. Finally, a numerical example that consists of solving the inverse/forward displacement analysis as well as the forward acceleration analysis of the end-effector platform is presented. The example also includes the computation of the workspace and the direct/inverse singularities of the example.

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Forward Displacement Analysis of a Class of the 6-6 Stewart Platforms

22nd Biennial Mechanisms Conference: Robotics, Spatial Mechanisms, and Mechanical Systems ◽

10.1115/detc1992-0205 ◽

1992 ◽

Author(s):

Wang Guozhen

Keyword(s):

Theoretical Result ◽

Special Form ◽

Closed Form Solution ◽

Form Solution ◽

Forward Displacement ◽

Displacement Analysis ◽

Quadratic Curve ◽

Prismatic Joints ◽

Base Platform ◽

Forward Displacement Analysis

Abstract In this paper, a special form of the Stewart platform, namely, that in which the top platform and base platform are similar and corresponding vertices are connected by six prismatic joints, is presented. We have developed the closed-form solution for the forward displacement analysis of this mechanism. When the six vertices of top platform are in a quadratic curve, this mechanism becomes singular. This new theoretical result has been confirmed by numerical example.

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A parallel manipulator inspired by the original Stewart platform

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406212454970 ◽

2012 ◽

Vol 227 (4) ◽

pp. 831-844 ◽

Cited By ~ 3

Author(s):

J Gallardo-Alvarado ◽

MA García-Murillo

Keyword(s):

Kinematic Analysis ◽

Parallel Manipulator ◽

Screw Theory ◽

Closed Form Solution ◽

Form Solution ◽

Flight Simulator ◽

Input Output ◽

Forward Displacement ◽

Numerical Examples ◽

Forward Displacement Analysis

This study addresses the kinematics of a new parallel manipulator inspired by the eight-bar linkage proposed as a flight simulator by Stewart almost five decades ago. Due to its partially decoupled topology, the forward displacement analysis of the robot is obtained in a nearly closed-form solution. The input–output equations of velocity and acceleration of the manipulator are systematically derived by resorting to reciprocal-screw theory. Numerical examples are included in the contribution in order to show the application of the method of kinematic analysis. As far as the authors are aware, the topology proposed in this contribution has not been reported in previous works.

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Forward Displacement Analysis of a Parallel Manipulator

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.217-218.1061 ◽

2011 ◽

Vol 217-218 ◽

pp. 1061-1065

Author(s):

Xi Guang Huang

Keyword(s):

Closed Form ◽

Parallel Manipulator ◽

Algebraic Method ◽

Polynomial Equation ◽

Forward Displacement ◽

Displacement Analysis ◽

Closed Form Solutions ◽

Displacement Problem ◽

Forward Displacement Analysis

A new algebraic method for the solution of the forward displacement analysis of a parallel manipulator is presented in this paper. Based on the algebraic method, the problem of the forward displacement problem is reduced to a polynomial equation in a single unknown from a constructed matrix which is relative small in the size. From the univariate equation, all closed-form solutions of the different locations of the mechanism can be derived.

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Forward Displacement Analysis of Three New Classes of Analytic Spherical Parallel Manipulators

Volume 1A: 25th Biennial Mechanisms Conference ◽

10.1115/detc98/mech-5953 ◽

1998 ◽

Author(s):

Xian-Wen Kong

Keyword(s):

Characteristic Polynomial ◽

Parallel Manipulator ◽

Parallel Manipulators ◽

Dual Solutions ◽

Fourth Degree ◽

Forward Displacement ◽

Displacement Analysis ◽

The Third ◽

Spherical Parallel Manipulator ◽

Forward Displacement Analysis

Abstract The analytic manipulator is a manipulator the characteristic polynomial of which is of fourth degree or lower. Three new classes of analytic spherical parallel manipulators with prismatic actuators are proposed. The first is the spherical parallel manipulator with non-similar planar platforms, the second is the spherical parallel manipulator with similar planar platforms, and the third is the spherical parallel manipulator with orthogonal platforms. The forward displacement analysis of these new classes of spherical parallel manipulators is investigated in sequence. Polynomials of degree 4, 2 and 2 in one unknown respectively can be obtained to inscribe this problem. Due to dual solutions of other unknowns, a maximum of eight solutions might be possible for each of the new analytic spherical parallel manipulators.

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